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Home » Solve the exponential equation \( 2^3x = 64 \). - Abu Waleed Tea

Solve the exponential equation \( 2^3x = 64 \). - Abu Waleed Tea

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Case \( m = 3 \):

📌 R’s in {1,2}, need to choose 2 → \(\binom{2}{2} = 1\) way

📌 \( n \geq m+1 = 4 \), and \( n \leq 5 \), so \( n = 4 \) or \( 5 \)

📌 For each \( n \), L’s in positions ≥ n, choose 2 → number of ways: \(\binom{6 - n}{2}\)

📌 \( n = 4 \): 6−4=2 → \(\binom{2}{2} = 1\)

📌 \( n = 5 \): 6−5=1 → \(\binom{1}{2} = 0\)

📌 So only \( n = 4 \): 1 way

📌 T is in the remaining position: once R’s and L’s are placed, T is fixed

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